Abstract
In three dimensional Riemannian space forms, introducing a natural moving frame, we define the associate curve of a curve and study the properties and relations of a curve and its associate curve. We state necessary and sufficient condition that a Frenet curve is a Bertrand curve in three dimensional Riemannian space forms, especially in a Riemannian 3-dimensional sphere and in a 3-dimensional hyperbolic space, resp. At the same time we give an explicit expression of the partner curve of a Bertrand curve.
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